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Home Applications of the Integral Averages Theorem 1: Average Slope
 
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Theorem 1: Average Slope

Recall that in Section 3.8, we defined the average slope of a function F between a and b as the quotient

average slope =06_applications_of_the_integral-274.gif

Using the Fundamental Theorem of Calculus we can find the connection between the average value of F' and the average slope of F.

THEOREM 1

Let F be an antiderivative of a continuous function f on an open interval I. Then for any a < b in I, the average slope of F between a and b is equal to the average value of f between a and b,

06_applications_of_the_integral-275.gif

PROOF
By the Fundamental Theorem,

06_applications_of_the_integral-276.gif
Home Applications of the Integral Averages Theorem 1: Average Slope

Last Update: 2006-11-05